CÁLCULO/4. DERIVADAS/1 Algebra de derivadas RA5 3.3 Derivada de la división entre un polinomio y un logaritmo. (EVALUACIÓN) Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mrow»«mi»#X«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«/mrow»«mi»#pol1«/mi»«/mfrac»«/math». Entonces, #Z

#GRAF

Obs.: Puede ingresar la respuesta exacta o la respuesta aproximada considerando 6 decimales de precisión.

]]> Solución:

La función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mrow»«mi»#X«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«/mrow»«mi»#pol1«/mi»«/mfrac»«/math», corresponde a un cuociente de funciones, por lo tanto, aplicaremos la regla de la derivada del cuociente (división) de funciones:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mfrac»«mrow»«mi»h«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«mrow»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfrac»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»h«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«mo»·«/mo»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»-«/mo»«mi»h«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»·«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mrow»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/math»

Aplicando la regla a nuestra función:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mfrac»«mrow»«mi»d«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»ln«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#pol1«/mi»«mo»)«/mo»«mo»-«/mo»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«mfrac»«mrow»«mi»d«/mi»«mfenced»«mi»#pol1«/mi»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«/mrow»«msup»«mfenced»«mi»#pol1«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/math»

Aplicando la derivada de del logaritmo natural y la derivada de una potencia:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mfenced»«mfrac»«mn»1«/mn»«mi»#X«/mi»«/mfrac»«/mfenced»«mo»(«/mo»«mi»#pol1«/mi»«mo»)«/mo»«mo»-«/mo»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«mfenced»«mrow»«mi»#pol2«/mi»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mi»#pol1«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mfenced»«mfrac»«mn»1«/mn»«mi»#X«/mi»«/mfrac»«/mfenced»«mo»(«/mo»«mi»#pol1«/mi»«mo»)«/mo»«mo»-«/mo»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«mfenced»«mi»#pol3«/mi»«/mfenced»«/mrow»«msup»«mfenced»«mi»#pol1«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«/mtable»«/math»

Desarrollando:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mfrac»«mrow»«mi»#pol1«/mi»«mo»-«/mo»«mi»#X«/mi»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«mfenced»«mi»#pol3«/mi»«/mfenced»«/mrow»«mi»#X«/mi»«/mfrac»«msup»«mfenced»«mi»#pol1«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mrow»«mi»#pol1«/mi»«mo»-«/mo»«mi»#X«/mi»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«mfenced»«mi»#pol3«/mi»«/mfenced»«/mrow»«mrow»«mi»#X«/mi»«msup»«mfenced»«mi»#pol1«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mrow»«/mfrac»«/mtd»«/mtr»«/mtable»«/math»

Por lo tanto:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»#X«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mrow»«mi»#pol1«/mi»«mo»-«/mo»«mi»#X«/mi»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mi»#X«/mi»«/mfenced»«mfenced»«mi»#pol3«/mi»«/mfenced»«/mrow»«mrow»«mi»#X«/mi»«msup»«mfenced»«mi»#pol1«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mrow»«/mfrac»«/mtd»«/mtr»«/mtable»«/math»
Luego, podemos evaluar en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#X«/mi»«mo»=«/mo»«mi»#x1«/mi»«/math»:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mfenced»«mrow»«mi»#x1«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»d«/mi»«mi»#X«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»#pol4«/mi»«mo»-«/mo»«mi»#x1«/mi»«mo»§nbsp;«/mo»«mi mathvariant=¨normal¨»ln«/mi»«mfenced»«mrow»«mi»#x1«/mi»«/mrow»«/mfenced»«mo»§nbsp;«/mo»«mfenced»«mrow»«mi»#pol5«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mi»#x1«/mi»«mo»§nbsp;«/mo»«msup»«mfenced»«mrow»«mi»#pol4«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mrow»«/mfrac»«/math»

Al desarrollar la última expresión (labor que dejaremos al estudiante) se obtiene que:

]]> 1.0000000 1.0000000 0 0 #resultado ¡Excelente!]]> #sol10 Revisa el desarrollo para identificar tus errores. ¡Tú puedes!

]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>w</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AUX</mi><mo>=</mo><mi>X</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math 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open="&verbar;"><mi>A</mi></mfenced><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol5</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>-</mo><mo>#</mo><mn>1</mn><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mn>2</mn><mo>*</mo><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>B</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>#</mo><mn>3</mn><mo>&quot;</mo><mo>,</mo><mi>pol1</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mfenced><mn>1</mn></mfenced><mo>&quot;</mo><mo>,</mo><mi>pol2</mi><mo>,</mo><mi>B</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol3</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>pol3</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol4</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>pol4</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol5</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>pol5</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr></mtable><mtable><mtr><mtd><mi>pol1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>#</mo><mn>3</mn><mo>&quot;</mo><mo>,</mo><mi>pol1</mi><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><mi>B</mi></mfenced><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mfenced><mn>1</mn></mfenced><mo>&quot;</mo><mo>,</mo><mi>pol2</mi><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><mi>B</mi></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol3</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>pol3</mi><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><mi>B</mi></mfenced><mo>,</mo><mi>X</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol4</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>pol4</mi><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><mi>B</mi></mfenced><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol5</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>pol5</mi><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><mi>B</mi></mfenced><mo>,</mo><mi>x1</mi></mrow></mfenced></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>C</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>pol1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>pol1</mi><mo>,</mo><mi>C</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mfenced><mn>0</mn></mfenced><mo>&quot;</mo><mo>,</mo><mi>pol2</mi><mo>,</mo><mi>C</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol4</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>pol4</mi><mo>,</mo><mi>C</mi></mrow></mfenced></mtd></mtr></mtable><mtable><mtr><mtd><mi>pol1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>pol1</mi><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><mi>C</mi></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mfenced><mn>0</mn></mfenced><mo>&quot;</mo><mo>,</mo><mi>pol2</mi><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><mi>C</mi></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>pol4</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><mi>pol4</mi><mo>,</mo><mfenced close="&verbar;" open="&verbar;"><mi>C</mi></mfenced></mrow></mfenced></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi><mo>=</mo><mi>dq1</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valorresultado</mi><mo>=</mo><mi>a_decimal</mi><mfenced><mrow><mi>redondear</mi><mfenced><mrow><mi>resultado</mi><mo>*</mo><mn>1000000</mn></mrow></mfenced><mo>/</mo><mn>1000000</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inf</mi><mo>=</mo><mi>a_decimal</mi><mfenced><mfenced><mrow><mfenced close="⌋" open="⌊"><mrow><mi>resultado</mi><mo>*</mo><mn>100000</mn></mrow></mfenced><mo>/</mo><mn>100000</mn></mrow></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sup</mi><mo>=</mo><mi>a_decimal</mi><mfenced><mfenced><mrow><mfenced close="⌉" open="⌈"><mrow><mi>resultado</mi><mo>*</mo><mn>100000</mn></mrow></mfenced><mo>/</mo><mn>100000</mn></mrow></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test1</mi><mfenced><mi>x</mi></mfenced><mo>:=</mo><mfenced><mrow><mi>x</mi><mo>&ges;</mo><mi>inf</mi><mo>∧</mo><mi>x</mi><mo>&les;</mo><mi>sup</mi></mrow></mfenced><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test2</mi><mfenced><mi>x</mi></mfenced><mo>:=</mo><mfenced><mrow><mi>x</mi><mo>&lt;</mo><mi>inf</mi><mo>∨</mo><mi>x</mi><mo>&gt;</mo><mi>sup</mi></mrow></mfenced><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>X</mi><mo>=</mo><mi>x1</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>&quot;</mo><mi>es</mi><mo> </mo><mi>igual</mi><mo> </mo><mi>a</mi><mo>:</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>vale</mi><mo>:</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y3</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>f</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>&quot;</mo><apply><diff/><bvar><mrow><mo>#</mo><mn>2</mn></mrow></bvar><mrow><mi>f</mi><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced></mrow></apply><mo>=</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>X</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z3</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>pendiente</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>recta</mi><mo> </mo><mi>tangente</mi><mo> </mo><mi>a</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z4</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>evaluación</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>derivada</mi><mo> </mo><mi>de</mi><mo> </mo><mo>#</mo><mn>3</mn><mo> </mo><mi>en</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mo>#</mo><mn>2</mn><mo>&quot;</mo><mo>,</mo><msub><mi>Y1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>Y2</mi><mo>,</mo><msub><mi>Y3</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>Z1</mi><mo>,</mo><mi>Z2</mi><mo>,</mo><mi>Z3</mi><mo>,</mo><mi>Z4</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mi>AUX</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mi>w</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mfenced><mrow><mn>2</mn><mi>w</mi></mrow></mfenced><mo>-</mo><mn>5</mn><mfenced><mn>1</mn></mfenced><mo>-</mo><mn>5</mn><mfenced><mn>0</mn></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mi>w</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msup><mfenced><mn>5</mn></mfenced><mn>2</mn></msup><mo>-</mo><mn>5</mn><mfenced><mn>5</mn></mfenced><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mfenced><mn>5</mn></mfenced><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0.0086388</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mo>-</mo><mn>8</mn><mo>*</mo><mi>w</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mi>ln</mi><mfenced><mi>w</mi></mfenced></mrow><mrow><mn>16</mn><mo>*</mo><msup><mi>w</mi><mn>4</mn></msup><mo>-</mo><mn>40</mn><mo>*</mo><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><mn>15</mn><mo>*</mo><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><mn>50</mn><mo>*</mo><mi>w</mi><mo>+</mo><mn>25</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>4</mn><mo>*</mo><msup><mi>w</mi><mn>3</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>w</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>w</mi></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #resultado </correctAnswer><correctAnswer type="mathml"> #sol10 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_function" correctAnswer="0"><param name="name">test1</param></assertion><assertion name="equivalent_function" correctAnswer="1"><param name="name">test2</param></assertion></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question>